Skyrim does have insane amounts of content. I'm level 27, don't know how many dozens of hours played, a zillion quests pending on my log, and I've barely started the main quest. And I haven't seen a single dragon yet.
I think you need to do the first quest for the Jarl of Whiterun before random dragon encounters start happening (this quest is kindof your introduction to dragon-slaying). That's just a guess, though.